Goulden, I. P.; Jackson, D. M.; Vainshtein, A. The number of ramified coverings of the sphere by the torus and surfaces of higher genera. (English) Zbl 0957.58011 Ann. Comb. 4, No. 1, 27-46 (2000). The main theme of the paper is to derive an explicit expression for the number of ramified coverings of the sphere by the torus with given ramification type for a small number of ramification points. The author conjectures this to be satisfied for an arbitrary number of ramification points. Reviewer: Th.M.Rassias (Athens) Cited in 2 ReviewsCited in 33 Documents MSC: 58D29 Moduli problems for topological structures 58C35 Integration on manifolds; measures on manifolds 05C30 Enumeration in graph theory 05E05 Symmetric functions and generalizations Keywords:ramified \(N\)-fold covering; sphere; Hurwitz relation; conjugacy class; partition; symmetric generating series PDF BibTeX XML Cite \textit{I. P. Goulden} et al., Ann. Comb. 4, No. 1, 27--46 (2000; Zbl 0957.58011) Full Text: DOI